Counterexamples & Disproof
📋 What it is
A counterexample is a single case that makes a general claim false — one is enough to disprove it.
🗣️ Coach says
To knock down a “for all” claim, you don’t argue — you just find ONE case where it fails. That one case is a counterexample, and it settles the matter completely. Finding the right case is the whole skill.
🧠 Memory hook
One counterexample kills a “for all”. You don’t need many — you need one.
😂 Giggle
What did the hypothesis say to the conclusion?
"I'm the starting point — you're where we end up!"
😲 Whoa!
Whole research programs have been ended by a single well-chosen counterexample — a claim believed for years can fall to one number.
✅ Quick check: Claim: “Every number that ends in 5 is prime.” Give a counterexample.
Say your answer out loud first — then reveal.
25 ends in 5 but equals 5 × 5, so it isn’t prime — one case disproves the whole claim.
A universal claim is false as soon as a single instance violates it.
🧪 Try it! (2 minutes)
Disprove “all four-sided shapes are squares” with the fastest counterexample you can draw.